1. Field of the Invention
This invention relates generally to the field of seismic interpretation, and more particularly, to modeling the restoration of a seismic fault.
2. Description of the Related Art
Faults in the crust of the earth cut through the sedimentary strata and offset them. Consequently, the seismic features in a 3D seismic dataset are often broken at faults. Seismic interpreters often struggle to correctly correlate features in a formation resulting from seismic events across a fault. A seismic fault can distort the depositional characteristics of a formation and even obscure hydrocarbon reservoirs that may be present and recoverable. Therefore, a way to image seismic formations that effectively compensates in reverse for fault movement is highly desirable. An advantageous result of such a method would provide a representation of the seismic formation that is restored to the pre-faulting state. Such a virtual reversal, or restoration, of a fault line may also reveal characteristics of the geological deposition and aid in identifying and locating hydrocarbon reservoirs. Thus 3D fault restoration involves removing the offset of seismic features in a 3D volume in order to facilitate the study of faulting sequences and in result, analyzing pre-faulting depositional environments.
The throw of a fault at the crossing of an event (e.g., an interpreted horizon) may be defined as the offset introduced into that event (in cross section) by the fault. Such an offset defines a slip vector at that point on the fault face. Event offsets may differ along the fault face; i.e., the slip vectors are not constant. Reversing a fault in general requires, therefore, the calculation of slip vectors at several events in the cross section.
Fault faces and the borders of a cross-section define the boundary of a mechanical continuum. When a load, in terms of traction or displacement (slip) vector, is applied to the boundary such as a fault surface, each point in the continuum will be displaced. The continuum will be deformed. Elasticity theory states that at equilibrium under loading, the total strain energy of the deformed region is—among all possible deformation for the given load—at a minimum. Or, equivalently, the theory states that the virtual work done by any admissible deformation is zero.
Rutten (Rutten, Kees, The Slokkert Validator Documentation, Landmark Graphics Internal Technical Communication, 2002) presented an algorithm to solve the same problem of fault restoration. When a number of slip vectors on a fault trace were given to reverse faulting, Rutten used a piecewise linear function to define the slip function on the fault surface. The approach is known as the “slip-parallel deformation model” in structural geology. In that method, the vertical displacement is attenuated, moving away from the fault, by applying a simple decay function along a set of scan lines intersecting with the fault. The results of that approach, although they may appear visually reasonable in 2-D views, lack a mechanics-based foundation. Additionally, the dispersion formulation may be complicated in practice for 3-D cases.
Elasticity theory combined with finite element methods or boundary element methods have been used to study the mechanics of faulting process (see Wei, K. and De Bremaecker, J.-Cl., A Replacement for the Coulomb-Mohr Criterion, Geophysical Research Letters, 19, 1033-1036, 1992; Wei, K. and De Bremaecker, J.-Cl., Fracture Under Compression: The Direction of Fracture Initiation, International Journal of Fracture, 61, 267-294, 1993; Wei, K. and De Bremaecker, J.-Cl., Fracture Growth Under Compression, Journal of Geophysical Research, 99, 13871-13790, 1994; Wei, K. and De Bremaecker, J.-Cl., Fracture Growth-I. Formulations and Implementations, Geophysical Journal International, 122, 735-745, 1995; Wei, K. and De Bremaecker, J.-Cl., Fracture Growth-II. Case Studies, Geophysical Journal International, 122, 746-754, 1995). The focus of these studies was to understand the orientation of fault growth for a given loading. However, solving the problem of 3D fault restoration is not the same problem as understanding how a fault grows. Therefore, fault growth models are of limited significance in 3D fault restoration—even when the goal of the restoration is to provide a mechanically sound method.
The problem of restoring a fault line is not trivial to solve because a restoration must be obtained in a mechanically and geologically plausible manner. In other words, the restoration model for displacement on the fault surface (i.e., for reversing a faulting event) must provide for dispersing mechanical energy to other parts of the region in consistency with a coherent mechanical model. The model should generally be based on assumptions that are available for validation, although it must be remembered that the goal of the restoration is not a reverse modeling of the actual faulting event.
Additionally, it would be useful if such a restoration of a seismic fault could be performed in an interactive manner, such that numerous iterations of various parameters and assumptions could be tested in an economically feasible timeframe.
Furthermore, the desirable method should provide the ability to perform a transformation on fault data in 3D, at least because 3D solutions for fault restoration are closer to geological reality and provide more accurately restored structures than 2D restorations. For 3D fault reversal problems, existing methods (such as the displacement extrapolation with scan lines) are overly simplified and cannot handle the infinite combinations of the azimuth and dip of the fault surface. The applications of 3D fault restoration are basically the same as for 2D fault restorations (see Wei, K. and Maset, R., Fast Fault Reversal, Expanded Abstract of 75th Annual International Meeting, Society of Exploratory Geophysics, Expanded Abstracts, 24, 767-770, 2005), namely for validating the correlations of interpreted horizons, for studying the structural geology, and for interpreting pre-faulting stratigraphy. However, the advantage of a 3D restoration is that out-of-plane slip vectors can be appropriately taken into account. (Note that horizon is a term that refers to a sub-surface, usually is the top or bottom of a deposition layer, which was continuous before faulting. When a faulting occurred, a horizon was broken into two pieces on each side of the fault.)
An example of a prior art method illustrating a 2D restoration is shown in FIG. 1. The fault is represented by the slip between sections 101 and 103. A horizon is shown as layer 104. 2D plane 102 intersects the formation parallel to line A′A 108. The slip surfaces of the fault are given by 105 and 106. FIG. 1 illustrates, that even in this simple case, the out-of-plane slip vector of the faulting cannot be accurately accounted for by applying a 2D restoration, such as given by plane 102. Typical faults are vastly more complex than as shown in FIG. 1; thus a 2D restoration method is very limited in scope, and ergo usefulness.
Thus, for accurately restoring the state near a fault to conditions before the fault occurred, a 3D numerical method is required for performing the necessary calculations that is computationally efficient, and whose assumptions and models are mathematically and mechanically valid.